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By Theorem~1.12 of the paper "A Class of Representations of Hecke Algebras",if $W$ is a Coxeter group whose proper parabolic subgroups are finite, and ifthe module of a finite $W$-digraph $\Gamma$ is isomorphic to the module of a$W$-graph, then $\Gamma$ must be acyclic. Here we extend this result to Coxetergroups with finite dihedral parabolic subgroups and $W$-graphs with arbitraryscalar edge labels. Also, errata for the paper are listed in the last section.

An extension of a theorem and errata for "A Class of Representations of Hecke Algebras"